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SIGMA 9 (2013), 016, 19 pages arXiv:1302.6000
https://doi.org/10.3842/SIGMA.2013.016
Contribution to the Special Issue “Geometrical Methods in Mathematical Physics”
A Generalization of the Hopf-Cole Transformation
Paulius Miškinis
Department of Physics, Faculty of Fundamental Sciences,
Vilnius Gediminas Technical University, Saulėtekio Ave 11, LT-10223, Vilnius-40, Lithuania
Received June 04, 2012, in final form February 17, 2013; Published online February 25, 2013
Abstract
A generalization of the Hopf-Cole transformation and its relation
to the Burgers equation of integer order and the diffusion
equation with quadratic nonlinearity are discussed.
The explicit form of a particular analytical solution is presented.
The existence of the travelling wave solution and the interaction of
nonlocal perturbation are considered.
The nonlocal generalizations of
the one-dimensional diffusion equation with quadratic nonlinearity and
of the Burgers equation are analyzed.
Key words:
nonlocality; nonlinearity; diffusion equation; Burgers equation.
pdf (390 kb)
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